FHPKE based on multivariate discrete logarithm problem
نویسنده
چکیده
Previously I proposed fully homomorphic public-key encryption (FHPKE) based on discrete logarithm problem which is vulnerable to quantum computer attacks. In this paper I propose FHPKE based on multivariate discrete logarithm assumption. This encryption scheme is thought to withstand to quantum computer attacks. Though I can construct this scheme over many non-commutative rings, I will adopt the FHPKE scheme based on the octonion ring as the typical example for showing how this scheme is constructed. The multivariate discrete logarithm problem (MDLP) is defined such that given f(x), g(x), h(x) and a prime q, final goal is to find m0, m1, n0, n1∈Fq* where h(x)=f ^m0(g^n0(x))+f ^m1(g^n1(x)) mod q over octonion ring. keywords: fully homomorphic public-key encryption, multivariate discrete logarithm problem, octonion ring, post quantum cryptography
منابع مشابه
FHPKE with Zero Norm Noises based on DLA&CDH
In this paper I propose the fully homomorphic public-key encryption(FHPKE) scheme with zero norm noises that is based on the discrete logarithm assumption(DLA) and computational Diffie–Hellman assumption(CDH) of multivariate polynomials on octonion ring. Since the complexity for enciphering and deciphering become to be small enough to handle, the cryptosystem runs fast. keywords: fully homomorp...
متن کاملFHE with Recursive Ciphertext
In this paper I propose fully homomorphic public-key encryption (FHPKE) with the recursive ciphertex. A ciphertext consists of three sub-ciphertexts corresponding to one plaintext. When we execute the additional operation or multiplicative operation, a new three sub-ciphertexts are generated from the three sub-ciphertexts recursively without revealing the plaintexts. The scheme is based on the ...
متن کاملThe new protocol blind digital signature based on the discrete logarithm problem on elliptic curve
In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve...
متن کاملAn efficient blind signature scheme based on the elliptic curve discrete logarithm problem
Elliptic Curve Cryptosystems (ECC) have recently received significant attention by researchers due to their high performance such as low computational cost and small key size. In this paper a novel untraceable blind signature scheme is presented. Since the security of proposed method is based on difficulty of solving discrete logarithm over an elliptic curve, performance of the proposed scheme ...
متن کاملGeneralized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2017 شماره
صفحات -
تاریخ انتشار 2017